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Honors Algebra 2 > Spring Final > Flashcards

Spring Final Flashcards

1
Q

Arithmetic Sequence

A

A sequence in which the difference of consecutive terms is constant

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2
Q

Asymptote

A

A line that a graph approaches more and more closely

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3
Q

Change of base formula

A

A formula that allows you to rewrite a logarithm in terms of logs written with another base

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4
Q

Circle

A

A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)

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5
Q

Combined Variation

A

A situation where a variable depends on other variables, and varies directly or inversely

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6
Q

Common Difference

A

The constant difference (d) between consecutive terms of an arithmetic sequence

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7
Q

Common Logarithm

A

A logarithm with base 10, denoted as log10, or simply just log

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8
Q

Common Ratio

A

The constant ratio (r) between consecutive terms of a geometric sequence

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9
Q

Completing the Square

A

To add a term (c) to an expression of the form x^2 + bx such that x^2 + bx + c is a perfect square trinomial

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10
Q

Complex Conjugates

A

Pairs of complex numbers of the forms a + bi and a - bi, where b does not equal 0

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11
Q

Complex Fraction

A

A fraction that contains a fraction in its numerator or denominator

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12
Q

Complex Number

A

A number written in the form a + bi, where a and b are real numbers

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13
Q

Composition of Functions

A

Operations that can be performed with 2 functions

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14
Q

Compound Inequality

A

2 inequality statements that are joined either by the word ¨or¨ or by the word ¨and¨ (¨and¨ would mean both statements are true).

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15
Q

Conic Section

A

A curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse

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16
Q

Consistent

A

If a liner or nonlinear system of equations has at least one set of values that satisfies each equation in the system, it is consistent (substituted into each equation while it still holds true as an identity)

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17
Q

Constant of Variation

A

The constant (a) in the inverse variation equation y = a/x, where a does not equal 0

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18
Q

Continuous Relation

A

A set of input values that consists of all numbers in an interval

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19
Q

Correlation Coefficient

A

A number (r) from -1 to 1 that measures how well a line fits a set of data pairs (x,y)

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20
Q

Dependent

A

Depends on the value of another number

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21
Q

Dimensions of a matrix

A

The dimensions of a matrix with (m) rows and (n) columns are m x n (read ¨m by n¨)

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22
Q

Direct Variation

A

Mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other

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23
Q

Discriminant

A

A parameter of an object or system calculated as an aid to its classification or solution. Also are defined for elliptic curves, finite field extensions, quadratic forms, and other mathematical entities

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24
Q

Ellipse

A

a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant, or resulting when a cone is cut by an oblique plane which does not intersect the base

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25
Q

End Behavior

A

The behavior of the graph of a function as x approaches positive infinity or negative infinity

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26
Q

Exponential Equation

A

An equation in which variable expressions occur as exponents

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27
Q

Extraneous Solution

A

A solution that is not a solution of the original equation

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28
Q

Extrema

A

Any point at which the value of a function is smallest or largest

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29
Q

Factor Theorem

A

A theorem linking factors and zeroes of a polynomial

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30
Q

Finite Sequence

A

A list of terms in a specific order. The sequence has a first term and a last term. The order of the terms follows some type of mathematical pattern or logical arrangement.

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31
Q

Function

A

An equation for which any x that can be plugged into the equation will yield exactly one y out of the equation; a special relationship where each input has a single output, and x is often the input value

32
Q

Geometric Sequence

A

A sequence in which the ratio of any term to the previous term is constant

33
Q

Greatest integer function

A

Also called step function, this is a piecewise function whose graph looks like the steps of a staircase. It is denoted by f(x) = [x] and is defined as the greatest integer less or equal to x.

34
Q

Growth Factor

A

The value of b in an exponential growth function of the form y = ab^x, where a > 0 and b > 1

35
Q

Hyberbola

A

A special arch-shaped curve that follows these rules

for any point, the distances:
from that point to a fixed point (the focus), and
from that point to a fixed straight line (the directrix)
are always in the same ratio.

It is one of the “Conic Sections”

36
Q

Identity Function

A

Also called an identity relation or identity map or identity transformation, it is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.

37
Q

Imaginary unit

A

The square root of -1, denoted i = the square root of -1

38
Q

Inconsistent

A

When a system has no solution, and the lines on the graphs do not intersect

39
Q

Independent

A

A variable in an equation that may have its value chosen freely without considering the values of other variables

40
Q

Infinite Sequence

A

An endless progression of numbers, which may include all the numbers of a particular set, or could be an arithmetic of geometric sequence

41
Q

Interval notation

A

A way to describe continuous sets of real numbers by the numbers that bound them. Meant to denote a specific point

42
Q

Inverse Functions

A

Functions that undo each other

43
Q

Inverse Relation

A

The set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function. If the graph of a function contains a point (a, b), then the graph of the inverse relation of this function contains the point (b, a).

44
Q

Inverse Variation

A

Two variables x and y show this when y = a/x, where a is not equal to 0

45
Q

Joint Variation

A

when a variable varies directly or inversely with multiple variables. For instance, if x varies directly with both y and z, we have x = kyz

46
Q

Latus rectum

A

The latus rectum of a conic section is the chord through a focus parallel to the conic section directrix

47
Q

Linear programming

A

A method of optimizing operations with some constraints. The main objective is to maximize or minimize the numerical value.

48
Q

Logarithm

A

a quantity representing the power to which a fixed number (the base) must be raised to produce a given number

49
Q

Logistic growth model

A

biological population with plenty of food, space to grow, and no threat from predators, tends to grow at a rate that is proportional to the population – that is, in each unit of time, a certain percentage of the individuals produce new individuals

50
Q

Matrix

A

a collection of numbers arranged into a fixed number of rows and columns

51
Q

nth root

A

used n times in a multiplication to get the original value. It is the general way of talking about roots

52
Q

Natural Logarithm

A

a number´s logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459

53
Q

Negative Exponent

A

how many times to divide the number by

54
Q

Parabola

A

a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves

55
Q

Parent Function

A

the simplest function of a family of functions that preserves the definition (or shape) of the entire family

56
Q

Piecewise defined function

A

a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain, and expresses the function rather than a characteristic of it in itself

57
Q

Point-slope form

A

the equation of a straight line in the form y − y1 = m(x − x1) where m is the slope of the line and (x1, y1) are the coordinates of a given point on the line

58
Q

Quadratic Function

A

a function that can be described by an equation of the form fx = ax2 + bx + c, where a ≠ 0

59
Q

Radicand

A

The value inside the radical symbol

60
Q

Rate of change

A

used to mathematically describe the percentage chance in a value over a defined period of time

61
Q

Rational exponent

A

An exponent that is also a fraction

62
Q

Rational function

A

any function which can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials

63
Q

Rationalizing the denominator

A

to eliminate any radical expressions in the denominator such as square roots and cube roots. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals

64
Q

Recursive formula

A

a formula that defines each term of a sequence using preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence

65
Q

Regression Line

A

an estimate of the line that describes the true, but unknown, linear relationship between the two variables. The equation of the regression line is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable

66
Q

Relative maximum

A

a point that is higher than the points directly beside it on both sides

67
Q

Relative minimum

A

a point that is lower than the points directly beside it on both sides

68
Q

Root

A

Where a function equals 0

69
Q

Scatter Plot

A

A graph of plotted points that show the relationship between two sets of data

70
Q

Sequence

A

an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members

71
Q

Set-builder notation

A

a shorthand used to write sets, often for sets with an infinite number of elements. It is used with common types of numbers, such as integers, real numbers, and natural numbers. This notation can also be used to express sets with an interval or an equation

72
Q

Step function

A

a function on the real numbers is this if it can be written as a finite linear combination of indicator functions of intervals

73
Q

Synthetic Division

A

a simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions

74
Q

Vertex Form

A

the alternate way of writing out a parabola for an equation

75
Q

Vertical line test

A

a visual way to determine if a curve is a graph of a function or not

76
Q

Zeros

A

When a function equals the value 0

Honors Algebra 2 (1 decks)

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